Ordination

We will use an RDA analysis with those three main components:

• Community matrix (C - Hellinger transformed)
• Environmental matrix (E)

So we ran the model:

rda.mod <- rda(C ~ ., as.data.frame(E))
rda.mod

## Call: rda(formula = C ~ day.cont + centrality + Size + dist.outlet
## + Treatment + Treat.Size + Treat.Size.Day, data =
## as.data.frame(E))
## 
##               Inertia Proportion Rank
## Total         0.24320    1.00000     
## Constrained   0.07771    0.31953    7
## Unconstrained 0.16549    0.68047    7
## Inertia is variance 
## Some constraints were aliased because they were collinear (redundant)
## 
## Eigenvalues for constrained axes:
##    RDA1    RDA2    RDA3    RDA4    RDA5    RDA6    RDA7 
## 0.05551 0.01210 0.00319 0.00284 0.00202 0.00152 0.00053 
## 
## Eigenvalues for unconstrained axes:
##     PC1     PC2     PC3     PC4     PC5     PC6     PC7 
## 0.04076 0.03462 0.02853 0.02347 0.01737 0.01483 0.00591

summary(rda.mod)$concont

## $importance
## Importance of components:
##                          RDA1   RDA2     RDA3     RDA4    RDA5     RDA6
## Eigenvalue            0.05551 0.0121 0.003188 0.002839 0.00202 0.001524
## Proportion Explained  0.71435 0.1557 0.041031 0.036530 0.02599 0.019617
## Cumulative Proportion 0.71435 0.8701 0.911096 0.947626 0.97362 0.993235
##                            RDA7
## Eigenvalue            0.0005257
## Proportion Explained  0.0067654
## Cumulative Proportion 1.0000000

The model show that our environmental matrix explains roughly 31% of the variance, which is not amazing but not so bad. The first axis explains 71% of that 31% and the second axis 16%.

We then ran a permutation ANOVA on the terms:

anova(rda.mod,by="terms",permu=200)

Here we can see that three variables are really standing out:

• Change in time
• Position in the landscape (centrality)
• Treatment (connected vs. isolated)

So it turns out that both the position in the landscape and resource pulse influence community position. Note that the interaction terms are also significant here indicating that the influence of the resource pulse on community composition vary as a function of the position in the network. The importance of these interaction terms in the model, however, remains fairly low compared to the main effects.

Let’s explore this model visually

First looking at the predictors (arrows) one can see that higher patch volume and high centrality values co-varies, which make sense since larger patches are generally more connected. In direct opposition (180 degrees on the figure) higher distance to outlet values are found which also make sense since smaller patches are mainly found upstream and thus further from the outlet. Orthogonal to this gradient (90 degree) is the effect of time. The species scores are well distributed on the plot as a function of the different constraints. Each point on the figure is a microcosm with the two colors identifying them as being part of a connected or an isolated blue ecosystem. From the model we know that the effect of the treatment is significant and relatively important. Here we can see that there is indeed some level of difference between sites in connected and isolated ecosystems.

Now in terms of interpretation, we can see that PCA and COL are more strongly associated with sites in connected ecosystem while Spi, Tet and Chi are associated with sites in isolated ecosystems. There are some interactions with other preditors though. For instance the figure suggest that PCA also became more abundant later in the experiment, while SPI was more abundant earlier suggesting some temporal community dynamics. Most interestingly, as mentionned, TET and CHI are associated with sites in isolated ecosystem, BUT also sites that tend to be more upstream in these ecosystems (smaller patch size more distant from the outlet). On the opposite ROT seems to be more associated to downstream sites (high centrality, high patch volume) independant of treatment or temporal aspect.

Log-ratio

Another useful way of representing those results is by using the log response ratio here defined has:

LRR = log( mean(connected) / mean(isolated) )

with confidence interval:

95CI = LRR +- 1.96 x SE(LRR)

In complementarity with the RDA model, let’s look at the log response ratio of the different protist species to the main treatment.

This figure conveys very similar information to the RDA figure: PCA and COL tend to be more abundant in microcosms from connected ecosystems while CHI, TET and BLE tend to be more abundant in microcosms from isolated ecosystems. GREAT!

Now let’s see if we can still detect the interaction with position in the network using patch size (which according to the RDA is the same as using distance to outlet or centrality):

Again, the same information is conveyed. We do see the interaction with PCA and COL being more abundant in the upstream (smaller volume) of the connected ecosystem, and CHI and TET being more abundant in the upstream (smaller volume) patches of the isolated ecosystem. For CHI this is also true for intermediate patch sizes.

Preliminary conclusion

The results presented above suggest that:

• Resource pulse from the green ecosystem does affect the structre of the community in the blue ecosystem by selecting for and againts some species
• This effect depend on the position in the blue spatial network and tend to be stronger in smaller, more isolated patches (based on patch volume, centrality and distance to the outlet)

Log-ratio

So there is a tendancy for bacteria density in the green ecosystem to be higher when connected to the blue ecosystem versus isolated controls. Let’s see if we can detect any interactions, even weak, with the position in the blue ecosystem:

Interestingly, the positive effect of being connected to the blue ecosystem is even across the green ecosystem no matter where they are connected in the dendritic network. It suggests that disperal along the lattice network act as a strong homogenizing force. There is an unsignificant trend here, nonetheless interesting, where the Effect size seems to follow a hump shape relationship with patch size. It is interesting because it somehow follow connectance in the blue ecosystem (middle patch size are most connected compared to smallest and largest):

Let’s explore those effects with a proper statistical model:

#Extract data 

X.bact <- data %>% 
  filter(day!=0 & Replicate %in% c("A","B")) %>% 
  mutate(Treatment = as.factor(Treatment),
         day = factor(day,levels=c("7","15","21","29")),
         day.cont = log(as.numeric(as.character(day))),
         Size = as.numeric(as.character(Size)),
         centrality = as.numeric(as.character(centrality)),
         dist.outlet = as.numeric(as.character(dist.outlet)))

#Run model (no log transformation based on histogramm of residuals)
  #Also: here Time was not significant so it was removed from the fixed variables
Mod4 <- nlme:::lme(bact.green ~ Treatment*Size + degree + bact.blue + prot.ab + prot.rich, 
                   random = ~ as.factor(day)|Replicate, data=X.bact,
                   method="ML",control=lmeControl(optimMethod="BFGS",maxIter=100,opt="optim"))
summary(Mod4)$tTable

##                                Value    Std.Error  DF    t-value
## (Intercept)             3.527976e+07 3.984232e+06 567  8.8548466
## TreatmentIsolated      -7.657812e+06 2.422733e+06 567 -3.1608148
## Size                    1.542833e+05 1.248515e+05 567  1.2357345
## degree                  2.322415e+05 7.777095e+05 567  0.2986225
## bact.blue               7.195793e-03 2.287006e-02 567  0.3146382
## prot.ab                 2.619464e+03 1.913583e+03 567  1.3688793
## prot.rich              -3.179406e+04 6.211282e+05 567 -0.0511876
## TreatmentIsolated:Size -3.371811e+04 1.463998e+05 567 -0.2303152
##                             p-value
## (Intercept)            1.071618e-17
## TreatmentIsolated      1.657254e-03
## Size                   2.170690e-01
## degree                 7.653375e-01
## bact.blue              7.531521e-01
## prot.ab                1.715791e-01
## prot.rich              9.591941e-01
## TreatmentIsolated:Size 8.179299e-01

From the model, we obtain the same information as with our LRR. There is a significant reduction of bacteria density in isolated green ecosystem compared to the ones connected to a blue ecosystem. Changes associated with size or degree are not significants.

Conclusion on aggregate metrics

We did not detect any effects of our main treatments in the Blue ecosystem on bacteria and protist densities or on protist richness. We did detect effects of patch size and changes over time. Those effects of patch size on aggegate metrics were thus independant of being connected or not and represent constraints of the dendritic spatial networks on richnes and density. Those patterns found here, especially on species richness, have already been analysed comprehensibly and published elsewhere (please see Harvey et al., Proc.B., in press)